A052354 - OEIS

%I #14 Apr 29 2019 03:18:40

%S 409,691,787,547,2053,139,4861,283,181,25087,337,709,2917,829,14197,

%T 919,3001,33589,2767,421,8221,1879,5179,1249,1471,10141,5011,20533,

%U 4483,54091,13249,4663,27883,5869,41443,8599,23311,9049,40699,82591

%N First primes of A031928 (lesser of 10-twins) with increasing distance to the next similar twin.

%C a(n) = p determines a prime quadruple [p, p+10, p+6n+6, p+6n+16] with difference pattern [10, 6n-4, 10].

%C The smallest distance between 10-twins [A052380(5)] is 12, while its increment is 6.

%F a(n) = p is the smallest of A031928 followed by the next 10- twin after a 6n+6 distance.

%e a(2)=691 results in [691,701,709,719] quadruple and [10,8,10] d-pattern without primes in the median gap;

%e a(10)=25087 yields [25087,25097,25153,25163] and [10,56,10] with 5 primes in the middle gap.

%Y Cf. A031928, A053323, A052380, A052381.

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 07 2000